Question

the force with which the earth attract an object above the surfaceof the earth varies inversly with the square of the distance of the object from the center of the earth. If an object 4000 miles from the center of the earthis attracted with a force of 160 pounds, find the force of attraction if the object were 6000 miles from the center of the earth.

Answer 1

If you don't want to get all physicsy with Newton's Law of gravitation, I recommend setting up a proportion.

Answer 2

Do you know the general form of an 'inverse proportion' / 'inverse variation?'

Answer 3

no

Answer 4

only need to figure out how to go about setting it up

Answer 5

Direct variation looks like this: \(y=kx\); inverse variation looks like this: \(y=k/x\).

Since you have force inversely proportional to distance, you can write: \(F=k/d^2\).
F := force, d := distance.

Answer 6

If you solve for k, you'll get

\(\large F_1d_1^2=F_2d_2^2\)

(via cross-multiplying the proportion and canceling the constant, k.)

Answer 7

You can now plug in all your known information to solve for the unknown \(F_2\)

Answer 8

ok thanks very much